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Procedure of the Galerkin Representation in Transversely Isotropic Elasticity

  • Dimitri V. GeorgievskiiEmail author
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

An algorithm for splitting an equilibrium displacement equation system with bulk forces for a transversely isotropic linearly-elastic medium is described that leads to three uncoupled equations with certain canonical fourth-order differential operators in the three components of the displacement vector. It is shown that, in the special case of isotropy, the proposed algorithm is mathematically equivalent to the Galerkin representation, well-known in the theory of elasticity.

References

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    Pobedria, B.E.: Numerical Methods in Theory of Elasticity and Plasticity. Moscow State University Publication, Moscow (1995) (in Russian)Google Scholar
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    Ashkenazi, E.K., Ganov, E.V.: Anisotropy of Structural Materials. Handbook. Mashinostroenie, Leningrad (1972) (in Russian)Google Scholar
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    Georgievskii, D.V.: An extended Galerkin representation for a transversely isotropic linearly elastic medium. J. Appl. Math. Mech. 79(6), 618–621 (2015)MathSciNetCrossRefGoogle Scholar
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    Georgievskii, D.V.: The Galerkin tensor operator, reduction to tetraharmonic equations, and their fundamental solutions. Dokl. Phys. 60(8), 364–367 (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussian Federation

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